On Wed, 2010-06-02 at 14:01 +1200, Richard O'Keefe wrote:
For what applications is it "useful" to use the same symbol for operations obeying (or in the case of floating point operations, *approximating* operations obeying) distinct laws?
If the given operations do share something in common. For example * is usually commutative. However you do use it with quaternions (Hamilton product). You even write ij = k despite the fact that ji = -k. I gave the code which might have work for both Integral and Fractional but it is not possible to type it in Haskell. Although I wouldn't mind something like: class Num a => Divisable a where (./.) :: a -> a -> a class (Real a, Enum a, Divisable a) => Integral a where div = (./.) ... class Divisable a => Fractional a where (/) = (./.) ... (/ and div preserve their meaning, ./. is the generalized division) Regards